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Bolgiano–Obukhov scaling in two-dimensional isotropic convection

Published online by Cambridge University Press:  18 May 2022

Jin-Han Xie Open the ORCID record for Jin-Han Xie [Opens in a new window]  and
Shi-Di Huang Open the ORCID record for Shi-Di Huang [Opens in a new window]
Jin-Han Xie
Affiliation:
Department of Mechanics and Engineering Science at College of Engineering, and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China Joint Laboratory of Marine Hydrodynamics and Ocean Engineering, Pilot National Laboratory for Marine Science and Technology (Qingdao), Shandong 266237, PR China
Shi-Di Huang
Affiliation:
Department of Mechanics and Aerospace Engineering and Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
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Abstract

The existence of Bolgiano–Obukhov (BO) scaling in Rayleigh–Bénard convection (RBC) has long been speculated. However, due to the inhomogeneity and anisotropy of the flow, and the lack of clear scale separation, no conclusive evidence has been found. To avoid these non-ideal factors, we construct an idealized isotropic convection system by introducing an additional horizontal buoyancy field to RBC in a doubly periodic domain. We focus on the two-dimensional case so that its upscale kinetic energy flux can enable a long inertial range for detecting the BO scaling. Through direct numerical simulations of this system, we justify the existence of BO scaling using second- and third-order structure functions, which are in good agreement with our theoretically obtained scaling relations from the Kármán–Howarth–Monin equations. These theoretical and numerical results provide direct support for the conjecture that the existence of the BO scaling in RBC is associated with the inverse kinetic energy cascade. For higher-order structure functions, we found strong intermittent effects in the buoyancy field, but not in the velocity. By comparing the present system with the canonical anisotropic RBC in a periodic domain, the effects of anisotropy on the scaling properties are elucidated.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A19
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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